Dynamics and Equilibration Mechanisms in Block Copolymer Particles

Abstract

Self-assembly of block copolymers into interesting and useful nanostructures, in both solution and bulk, is a vibrant research arena. While much attention has been paid to characterization and prediction of equilibrium phases, the associated dynamic processes are far from fully understood. Here, we explore what is known and not known about the equilibration of particle phases in the bulk, and spherical micelles in solution. The presumed primary equilibration mechanisms are chain exchange, fusion, and fragmentation. These processes have been extensively studied in surfactants and lipids, where they occur on subsecond time scales. In contrast, increased chain lengths in block copolymers create much larger barriers, and time scales can become prohibitively slow. In practice, equilibration of block copolymers is achievable only in proximity to the critical micelle temperature (in solution) or the order–disorder transition (in the bulk). Detailed theories for these processes in block copolymers are few. In the bulk, the rate of chain exchange can be quantified by tracer diffusion measurements. Often the rate of equilibration, in terms of number density and aggregation number of particles, is much slower than chain exchange, and consequently observed particle phases are often metastable. This is particularly true in regions of the phase diagram where Frank–Kasper phases occur. Chain exchange in solution has been explored quantitatively by time-resolved SANS, but the results are not well captured by theory. Computer simulations, particularly via dissipative particle dynamics, are beginning to shed light on the chain escape mechanism at the molecular level. The rate of fragmentation has been quantified in a few experimental systems, and TEM images support a mechanism akin to the anaphase stage of mitosis in cells, via a thin neck that pinches off to produce two smaller micelles. Direct measurements of micelle fusion are quite rare. Suggestions for future theoretical, computational, and experimental efforts are offered.

Mechanism of Escape of a Single Chain from a Diblock Copolymer Micelle

“…Solving for f gives (8) To determine the value of the free energy at some value of r, we substitute eq 8 into eq 6, which gives a free energy that is linear in r − r c and independent of N core , (9) The free energy will keep increasing until it is more favorable to extract the entire core block into the solvent rather than stretch further. Assuming that the core block is wetted by the solvent, the maximum in the free energy is (10) and the free energy barrier is linear with both N core and Δa, as seen in previous work. 38 The corresponding location r* of the chain junction at the maximum in the free energy is obtained by equating eqs 9 and 10: (11) The key prediction of this model is already evident in Figure 1; for a micelle formed by chains of a given size A x B 8 , the free energy for extracting a tracer chain of size A y B 8 should follow a similar trajectory with r, independent of the value of y, until reaching the point at which that core block size is fully Clearly, Figure 8a indicates that the radial distance of the transition state from the core radius of the micelle, r* − r c , varies linearly with N core of the tracer chain, consistent with eq 11.…”

“…The free energy will keep increasing until it is more favorable to extract the entire core block into the solvent rather than stretch further. Assuming that the core block is wetted by the solvent, the maximum in the free energy is F k T N a barrier B core (10) and the free energy barrier is linear with both N core and Δa, as seen in previous work. 38 The corresponding location r* of the chain junction at the maximum in the free energy is obtained by equating eqs 9 and 10:…”

“…As recently reviewed, 10 micelle relaxation was first described by the Aniansson−Wall model in the context of surfactant systems. 11 This model predicts that micelles equilibrate by a combination of single chain exchange, fusion, and fragmentation.…”

Geometry-Modulated Self-Assembly Structures of Covalent Polyoxometalate–Polymer Hybrid in Bulk and Thin-Film States

“…Considering that the thermal annealing time for KPOM-PS n and KPOM-2PS n was the same, the structure formation rate of KPOM-PS n with a smaller ε value is faster than that of KPOM-2PS n . From the perspective of kinetics, the formation rate of a particular long-range order structure in the diblock copolymer phase separation system depends on the free chain concentration and association–dissociation rates of chains in the microphase-separated domains. , For the LAM and HEX phases of KPOM-2PS n , the congestion of two PS chains per POM cluster at the interfaces would impede the self-adjustment of hybrid molecules by a diffusive process along the interface of microphase-separated domains, and thus, the structure formation kinetics is slower than KPOM-PS n samples. Besides, the hybrid molecules within discrete spherical domains have limited pathways for self-adjustment except for direct chain exchange between spherical domains, and therefore, the full development of spherical cubic phases would take even longer time than the LAM and HEX phases.…”

Effect of Changing Interfacial Tension on Fragmentation Kinetics of Block Copolymer Micelles

“…While the equilibrium micellar structures attained via self-assembly are relatively well studied, the understanding of the micelle formation and their equilibration processes is still incomplete. , To realize the full potential of BCP micelles, an extensive understanding of the dynamics of micelle formation and equilibration processes is essential to optimize structure–property relationships. The equilibration of surfactant micelles has been studied extensively. − For BCP micelles, theoretical description of the equilibration mechanism − is supported by a few experimental studies which generally focus on a single mechanism in isolation, such as chain exchange, − or fusion and fragmentation. , A comprehensive review of the dynamics and equilibration of BCP micelles along with the future scope and challenges has been presented in a recent review …”